Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances
This work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small p...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/174604 |
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| author | Hamid El Qarnia Fayssal El Adnani El Khadir Lakhal |
| author_facet | Hamid El Qarnia Fayssal El Adnani El Khadir Lakhal |
| author_sort | Hamid El Qarnia |
| collection | DOAJ |
| description | This work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small perturbation parameter: the Stefan number, ε. This analytical solution, which takes into account the effects of the superheating of PCM, finite height of the enclosure, thickness of the wall, and wall-solid shell interfacial thermal resistances, was expressed in terms of nondimensional temperature distributions of the bottom wall of the enclosure and both PCM phases, and the dimensionless solid-liquid interface position and its dimensionless speed. The developed solution was firstly compared with that existing in the literature for the case of nonsuperheating PCM. The predicted results agreed well with those published in the literature. Next, a parametric study was carried out in order to study the impacts of the dimensionless control parameters on the dimensionless temperature distributions of the wall, the solid shell, and liquid phase of the PCM, as well as the solid-liquid interface position and its dimensionless speed. |
| format | Article |
| id | doaj-art-96a6d4343150428fba658535a13c5f88 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-96a6d4343150428fba658535a13c5f882025-02-03T01:22:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/174604174604Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact ResistancesHamid El Qarnia0Fayssal El Adnani1El Khadir Lakhal2Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Fluid Mechanics and Energetics Laboratory, Affiliate to CNRST, URAC 27, P.O. Box 2390, Marrakesh, MoroccoDepartment of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Fluid Mechanics and Energetics Laboratory, Affiliate to CNRST, URAC 27, P.O. Box 2390, Marrakesh, MoroccoDepartment of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Automatic, Environmental and Transfer Process Laboratory, Affiliate to CNRST, URAC 28, P.O. Box 2390, Marrakesh, MoroccoThis work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small perturbation parameter: the Stefan number, ε. This analytical solution, which takes into account the effects of the superheating of PCM, finite height of the enclosure, thickness of the wall, and wall-solid shell interfacial thermal resistances, was expressed in terms of nondimensional temperature distributions of the bottom wall of the enclosure and both PCM phases, and the dimensionless solid-liquid interface position and its dimensionless speed. The developed solution was firstly compared with that existing in the literature for the case of nonsuperheating PCM. The predicted results agreed well with those published in the literature. Next, a parametric study was carried out in order to study the impacts of the dimensionless control parameters on the dimensionless temperature distributions of the wall, the solid shell, and liquid phase of the PCM, as well as the solid-liquid interface position and its dimensionless speed.http://dx.doi.org/10.1155/2012/174604 |
| spellingShingle | Hamid El Qarnia Fayssal El Adnani El Khadir Lakhal Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances Journal of Applied Mathematics |
| title | Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances |
| title_full | Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances |
| title_fullStr | Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances |
| title_full_unstemmed | Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances |
| title_short | Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances |
| title_sort | approximate analytical solution for one dimensional solidification problem of a finite superheating phase change material including the effects of wall and thermal contact resistances |
| url | http://dx.doi.org/10.1155/2012/174604 |
| work_keys_str_mv | AT hamidelqarnia approximateanalyticalsolutionforonedimensionalsolidificationproblemofafinitesuperheatingphasechangematerialincludingtheeffectsofwallandthermalcontactresistances AT fayssaleladnani approximateanalyticalsolutionforonedimensionalsolidificationproblemofafinitesuperheatingphasechangematerialincludingtheeffectsofwallandthermalcontactresistances AT elkhadirlakhal approximateanalyticalsolutionforonedimensionalsolidificationproblemofafinitesuperheatingphasechangematerialincludingtheeffectsofwallandthermalcontactresistances |